Abelian theorems

Abelian theorems

[ə′bēl·yən ′thir·əmz]
(mathematics)
A class of theorems which assert that if a sequence or function behaves regularly, then some average of the sequence or function behaves regularly; examples include the Abel theorem (second definition) and the statement that if a sequence converges to s, then its Cesaro summation exists and is equal to s.